Appraised value, and equity

[Chris Knebel]

If you find a beat up property selling for less than it's appraised value is it safe to say the difference (in what you pay and appraised)  is equity? 

A property:

Appraised value is $100,000, purchase price $80,000. Is that an instant $20,000 in equity? If it's purchased for $80,000, with $10,000 in repairs and now appraises for $150,000 is that now $60,000 in equity? Are their circumstances when that's not the case?

Thanks I'm new to BP. Appreciate the help.